The object of على is not ثياب بيضاء, but the pronoun ـه, so ثياب بيضاء is not governed by على.
The way the sentence breaks down is:
سائق السيارة: topic (nominative) with complement (genitive)
عليه ثياب بيضاء: predicate
The predicate is itself a clause with a topic and a predicate:
ثياب بيضاء: topic (nominative) with adjective (nominative)
عليه: predicate consisting of a preposition (no case) and object (genitive)
[Note that it's سائق, not سايق, in Modern Standard Arabic.]